| 非对称区间上调和函数的Schwarz引理 |
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| 引用本文： | 李孟华,陈行堤. 非对称区间上调和函数的Schwarz引理[J]. 华侨大学学报(自然科学版), 2017, 0(6): 898-902. DOI: 10.11830/ISSN.1000-5013.201612009 |
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| 作者姓名： | 李孟华 陈行堤 |
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| 作者单位： | 华侨大学 数学科学学院, 福建 泉州 362021 |
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| 摘 要： | 研究单位球到给定一般区间上的实调和函数的Schwarz型引理.运用调和函数的平均值定理,将像域在对称区间［-1,1］上的调和函数的Schwarz引理推广到在一般区间［a,b］上.作为一个应用,改进了Partyka和Sakan的一个结果,得到实调和函数的下界估计.
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| 关 键 词： | 调和函数 Schwarz引理 Poisson核 平均值定理 |
Schwarz Lemma for Harmonic Functionsin Asymmetric Interval |
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| LI Menghua,CHEN Xingdi. Schwarz Lemma for Harmonic Functionsin Asymmetric Interval[J]. Journal of Huaqiao University(Natural Science), 2017, 0(6): 898-902. DOI: 10.11830/ISSN.1000-5013.201612009 |
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| Authors: | LI Menghua CHEN Xingdi |
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| Affiliation: | School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China |
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| Abstract: | In this paper, we investigate the Schwarz lemma for real harmonic functions of the unit ball into a general interval. By appealing to the method of mean-value theorem of harmonic functions, we obtain the Schwarz lemma of harmonic functions with their image domains generalized from the symmetric interval ［-1,1］ to a general interval ［a,b］. As an application of this result, we improve the upper bound estimate given by Partyka and Sakan. Moreover, a lower bound for this class of harmonic functions is also given. |
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| Keywords: | harmonic mapping Schwarz lemma Poisson kernel mean-value theorem |
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